COSMOPOLITAN COLLEGE (GIRLS) INDEX NO:
FINAL YEAR INTERNAL EXAMINATIONS
Grade 10
MATHEMATICS Sept/Oct 2023
Paper 1 Time: 2 hours
You must answer on the question paper.
You will need: Geometrical instruments
INSTRUCTIONS
• Answer all questions.
• Use a black or dark blue pen.
• You may use an HB pencil for any diagrams or graphs.
• Write your name, centre number and candidate number in the boxes at the top of the page.
• Write your answer to each question in the space provided.
• Do not use an erasable pen or correction fluid.
• Do not write on any bar codes.
• Calculators must not be used in this paper.
• You may use tracing paper.
• You must show all necessary working clearly.
INFORMATION
• The total mark for this paper is 80.
• The number of marks for each question or part question is shown in brackets [ ].
• No student will be allowed to leave the examination room until allocated time is over.
1. (a) Write 0.07164 correct to 2 significant figures.
Answer ………………………[1]
(b) Change 6200 cm2 into m2.
Answer ………………………[1]
2. (a) Work out 15 cents as a percentage of 300 cents.
Answer ………………………[1]
(b) Find the value of 5𝑎 − 3𝑏 when a = 7 and b =-2.
Answer ………………………[2]
(c) Work out
!
(i) 125"
Answer ………………………[1]
2
𝟐 #𝟐
(ii) ! "
𝟑
Answer ………………………[2]
3.
3
4. Find the highest common factor (HCF) of 36 and 63.
Answer ………………………[2]
5.
(a) Ahmed increases 40 by 10%.
From this list put a ring around the correct calculation.
𝟒𝟎 × 𝟏𝟎 𝟒𝟎 × 𝟏. 𝟏 𝟒𝟎 × 𝟎. 𝟗 𝟒𝟎 × 𝟎. 𝟏
[1]
2
(b) Ahmed finds the magnitude of the vector - /
−3
From this list put a ring around the correct calculation.
√𝟐𝟐 + −𝟑𝟐 𝟐𝟐 − 𝟑𝟐 4𝟐𝟐 + (−𝟑)𝟐 𝟐𝟐 + (−𝟑)𝟐 √𝟐𝟐 + −𝟑𝟐
[1]
6. 8 9 1 3 12 7 6 2
Calculate the mean of these 8 numbers
Answer ………………………[2]
4
7.
8. (a) Solve the inequality
3𝑛 − 11 > 5𝑛 − 18
Answer ………………………[2]
(b) Factorise
(i) 4𝑥 " − 8𝑥𝑦
Answer ………………………[2]
(ii) 𝑥 " + 6𝑥 + 8
Answer ………………………[2]
5
(iii) 2𝑎𝑥 − 𝑎𝑦 + 6𝑏𝑥 − 3𝑏𝑦
Answer ………………………[3]
9.
10.
(a) Work out 0.095 as a fraction in its simplest form
Answer ………………………[1]
(b) Increase 42 kg in the ratio 5:3
Answer ………………………[1]
6
11. A glass of drink is made by adding water to 20 mililitres of orange juice.
(a) Anna is making a glass of this drink.
She uses the water to orange juice in the ratio 9:1.
Work out how much drink is in this glass in mililitres.
Answer ……………………ml [1]
(b) Tariq has a bottle containing 2 litres of orange juice.
He uses all of the orange juice to make glasses of this drink.
Work out the number of glasses that he makes.
Answer ………………………[2]
12. The line AB is one side of an equilateral triangle ABC.
Using a straight edge and compasses only, construct triangle ABC. C is found above line AB.
[2]
7
13.
8
14.
! # "
Work out
"
÷ &1 $ − %( .
You must show all your working and give your answer as a mixed number.
Answer ……………….…[3]
15.
9
16.
10
17.
11
18. (a) Write 0.000 0845 in standard form.
Answer …………………………….…[1]
(b) 𝑝 = 2.7 × 10## 𝑞 = 9 × 10#"
Evaluate the following.
Give each answer in standard form.
(i) 𝑝+𝑞
Answer …………………………….…[2]
(ii) 𝑝 ÷ 𝑞
Answer ………………………….…[2]
12
19.
13
20.
14
21.
The diagram shows sector AOB, with radius 6 cm. By using 𝜋 = 3.14 , find
(a) the length of arc AB
Answer ……………….…[3]
(b) the area of sector AOB
15
Answer ……………….…[3]
22.
The diagram shows a straight line intersecting two parallel lines.
Find the value of p and the value of q.
p = ………………………[1]
q = ………………………[1]
16
23.
17
